Department of Mathematics








A Dilation Theorem For Invariant Weakly Positive Semidefinite Kernels Valued In Admissible Spaces






Abstract: An ordered *-space Z is a complex vector space with a conjugate linear involution *, and a strict cone Z+ consisting of self-adjoint elements. An admissible space in the sense of Loynes is an ordered *-space with a complete locally convex topology, compatible with the  partial ordering of its cone. We consider weakly positive semidefinite kernels that are invariant under a left action of a *-semigroup and valued in an admissible space. Under a suitable boundedness condition we obtain VH (Vector Hilbert) space linearisations and equivalently, reproducing kernel VH-spaces and *-representations of the *-semigroup on them. As applications of the
main theorem, we obtain various known dilation theorems with a suitable choice of a kernel and an admissible space. This is a joint work with A. Gheondea.



Date:  Thursday, November 24, 2016

Time: 13:40

Place: Mathematics Seminar, SA-141



Tea and cookies will be served before the seminar.